Post on 16-Oct-2020
High thermopower and ultra low thermal conductivity inCd-based Zintl phase compounds
Tribhuwan Pandey1 and Abhishek K. Singh∗1
1Materials Research Centre, Indian Institute of Science, Bangalore-560012
1 PBE band structures:
Γ X S Y Γ Z U R -2
-1
0
1
2
En
erg
y(e
V)
Γ A H K Γ M L H T
EF
(a) (b)
(c) (d)
Γ A H K Γ M L H Γ A H K M L H -2
-1
0
1
2
Γ
En
erg
y(e
V)
EF
Figure S1: PBE band structures for (a) CdSb, (b) CaCd2Sb2, (c) SrCd2Sb2, and (d) BaCd2Sb2.
∗abhishek@mrc.iisc.ernet.in
1
Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics.This journal is © the Owner Societies 2015
2 Orbital decomposed density of states:
0
0.1
0.2
-4 -2 0 2 40
0.2
0.4
0.6
0
2
4 sp
d
0
1
2
3
0
1
2
0
0.2
0.4
0
0.2
0.4
0
0.2
0.4
-4 -2 0 2 40
0.4
0.8
-4 -2 0 2 40
0.4
0.8
-4 -2 0 2 40
0.4
0.8
DO
S (
arb .unit
)
CaCd2Sb
2SrCd
2Sb
2SCd
2Sb
2CdSb
Ca Sr Ba
Cd Cd Cd
Sb Sb Sb
Cd
Sb
Energy (eV)
Figure S2: Orbital decomposed density of states for CdSb, CaCd2Sb2, SrCd2Sb2, and BaCd2Sb2.
2
3 Anisotropy in thermopower:
-450
-300
-150
0
150
300
450
Sxx
Syy
Szz
-450
-300
-150
0
150
300
450
1018
1019
1020
-300
-150
0
150
300
1018
1019
1020
-450
-300
-150
0
150
300
450S
xx= S
yy
Szz
(n, p) cm-3 (n, p) cm-3
S (µ
V/K
)S
(µ
V/K
)
(a) (b)
(c) (d)
CdSb CaCd2Sb
2
SrCd2Sb
2BaCd
2Sb
2
Figure S3: Anisotropy in thermopower as a function of carrier concentration for (a) CdSb, (b) CaCd2Sb2,(c) SrCd2Sb2, and (d) BaCd2Sb2 at 300 K. The solid and doted lines denote results for p- and n-type chargecarriers.
3
4 Temperature dependence of thermopower at fixed doping levels:
0
100
200
300
400
8e+182e+196e+19
200 400 600 800T (K)
-400
-300
-200 -7e+18-9e+18-2e+19
S (µ
V/K
) 150
300
450
8e+182e+196e+19
T (K)
-450
-300
-150-7e+18-9e+18-2e+19
100
200
300
400
8e+182e+196e+19
250 500 750 1000T (K)
-300
-200
-100
0 -8e+18-2e+19-6e+19
S (µ
V/K
)
p-type
n-type
100
200
300
400
8e+182e+196e+19
250 500 750 1000T (K)
-300
-200
-100
0
-8e+18-2e+19-6e+19
n-type n-type
n-type
p-type
p-type p-type
250 500 750 1000
(a) (b)
(c) (d)
Figure S4: Thermopower as a function of temperature at optimised fixed doping levels for (a) CdSb, (b)CaCd2Sb2, (c) SrCd2Sb2, and (d) BaCd2Sb2 under p and n-type doping.
4
5 Effect of ionic radii on thermoelectric properties
400 800 1200
1
2
4
400 800 1200
-450
-300
-150
0
150
300
400 800 12000.0
0.5
1.0
1.5
2.0
σ/τ
(Ω
ms)
-1
S (µ
V/K
)
S2σ
/τ
CaCd2Sb
2
SrCd2Sb
2
BaCd2Sb
2
(a) (b) (c)
Figure S5: Transport coefficient (a) σ/τ , (b) S, and, (c) S2σ/τ as a function of temperature for CaCd2Sb2,SrCd2Sb2, and BaCd2Sb2 at a fixed doping level of 1×1019 cm−3. The direction of arrows in Fig. (a) and(b) represent the increasing ionic radii.
5
6 Temperature dependence of power factor at fixed doping levels:
0
0.7
1.4
2.1
2.8
8e+182e+196e+19
250 500 750 1000T (K)
0
0.7
1.4
2.1
2.8
-7e+18-9e+19-2e+19
p-type
n-type
0
1
2
3
4
8e+182e+196e+19
250 500 750 1000T (K)
0
2
4
6
-8e+18-2e+19-6e+19
p-type
n-type
0
1
2
3
4
8e+182e+196e+19
250 500 750 1000T (K)
0
1
2
3 -8e+18-2e+19-6e+19
p-type
n-type
0
1
28e+182e+196e+19
250 500 750 1000T (K)
0
1
2
3
4
-7e+18-9e+19-2e+19
p-type
n-type
(a) (b)
(c) (d)
S2σ
/τ (
10
11W
/mk
2s)
S2σ
/τ (
10
11W
/mk
2s)
Figure S6: Calculated power factor as a function of temperature at optimised fixed doping levels for (a)CdSb, (b) CaCd2Sb2, (c) SrCd2Sb2, and (d) BaCd2Sb2 under p and n-type doping.
6
7 Electronic structure and transport for PbTe and PbSe:The electronic structure calculations were performed within density functional theory (DFT) using thelinearised augmented plane-wave (LAPW) method with local orbitals (1, 2) as implemented in the WIEN2kcode (3). The LAPW sphere radii were set 2.5 for all the elements. In addition Rkmax = 9.0, is used to ensurethe well convergence of basis set where, R and kmax are the smallest LAPW sphere radius and interstitialplane-wave cutoff, respectively. The Brillouin zone was sampled by taking 5000 k-points for all crystalstructures. In order to obtain an accurate band gap we employ modified Becke Johnson functional (4, 5)of Tran and Blaha (TB-mBJ). The transport calculations were done using Boltzmann transport theory (6)within the constant scattering time approximation. We used BoltzTraP code (7) for transport calculationsby taking 40000 k-points in the irreducible Brillouin zone.
-4
-2
0
2
4
PbSe E
F
Γ W L WX KΓ
-4
-2
0
2
4
En
erg
y(e
V)
PbTe
W L WX K
(a) (b)
Figure S7: The band structure of PbTe (a) and PbSe (b) calculated with the TB-mBJ potentials. For bothband structures the energy zero is set to the valence band maximum. The calculated bandgap are in excellentagreement with the experimental values. These results were further used in transport calculation in order tocompare with Zintl phase. (See Figure 6 of the manuscript)
7
8 Dependence of lattice thermal conductivity on anharmonic scatter-ing rates and total scattering phase space
ω (rad/ps)
0.01
1.00
w (
ps-1
)
CdSbCaCd
2Sb
2
SrCd2Sb
2
BaCd2Sb
2
0 10 201.1
1.2
1.3
1.4
Ba Ca Sr
0.4
0.6
0.8
1.0
Ph
ase
spac
e (1
0-2)
κl (w
/m-K
)
κl @ 700 K
(a) (b)
Figure S8: (a) Anharmonic scattering rates of CdSb and ACd2Sb2 (A=Ca,Sr, and Ba) at 300 K vs angularfrequency ω. (b) Three phonon scattering phase space for ACd2Sb2 (A=Ca,Sr, and Ba). Note that BaCd2Sb2
exhibits highest scattering rate followed by CdSb, CaCd2Sb2, and SrCd2Sb2. This is similar to the trendobserved in Gruneisen parameters (γ).
9 Calculation of lattice thermal conductivity by Debye-Callawaymodel:
The Debye-Callaway model (8, 9, 10) approximates the lattice thermal conductivity as a function of Debyetemperatures (ΘD), phonon group velocities (v) and Gruneisen parameters (γ). Next we use these abovementioned quantities to parametrize the Debye-Callaway model and calculate the lattice thermal conduc-tivity. The resulting thermal conductivities are shown in Figure S9. When compared with the κl obtainedfrom iterative solution of Boltzmann transport equation (BTE) these values are quite over estimated. Thisis because Debye Callaway model severs as a upper limit to lattice thermal conductivity. This phenomenonis agreement other theoretical studied (11). The theoretically calculated thermal conductivity for CdSband CaCd2Sb2 captures the experimental trend an follows the order BaCd2Sb2 < CdSb < CaCd2Sb2 <SrCd2Sb2 which, is same as the trend obatined from BTE. The disagreement between experimental andtheoretical values can be attributed to the approximations inherent in the Debye-Callaway formalism.
8
κL (
W/m
K)
200 400 600 800 1000T (K)
0
2
4
6CdSbCaCd
2Sb
2
SrCd2Sb
2
CdSb-exp
PbTe-exp
CaCd2Sb
2
BaCd2Sb
2
Figure S9: Lattice thermal conductivity of CdSb and ACd2Sb2 (where A = Ca, Sr, Ba) as obtained byDebye Callaway model. The diamond, triangle and cross denote experimental values of CdSb, CaCd2Sb2
and PbTe, respectively. The points represent the calculated values.
References[1] Sjostedt, E.; Nordstrom, L.; Singh, D. J. Solid State Commun. 2000, 114, 15 – 20.
[2] Singh, D. J.; Nordstrom, L. Planewaves Pseudopotentials and the LAPW Method, 2nd ed.; Springer:Berlin, 2006.
[3] Blaha, P.; Schwarz, K.; Madsen, G. K. H.; Kvasnicka, D.; Luitz, J. WIEN2K, An Augmented PlaneWave + Local Orbitals Program for Calculating Crystal Properties; Karlheinz Schwarz, Techn. Uni-versitat Wien, Austria, 2001.
[4] Becke, A. D.; Johnson, E. R. J. Chem. Phys. 2006, 124.
[5] Tran, F.; Blaha, P. Phys. Rev. Lett. 2009, 102, 226401.
[6] Ziman, J. M. Principles of the Theory of Solids; Cambridge University Press: Cambridge, 1964.
[7] Madsen, G. K.; Singh, D. J. Comput. Phys. Commun. 2006, 175, 67 – 71.
[8] Callaway, J. Phys. Rev. 1959, 113, 1046–1051.
[9] Morelli, D. T.; Heremans, J. P.; Slack, G. A. Phys. Rev. B 2002, 66, 195304.
[10] Morelli, D. T.; Jovovic, V.; Heremans, J. P. Phys. Rev. Lett. 2008, 101, 035901.
[11] Ma, J.; Li, W.; Luo, X. Phys. Rev. B 2014, 90, 035203.
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